Hey, i have to complete an AS level core one maths exam paper but i am completely stuck on the following question: Solve the equation x6+26x3-27=0

I have nooooo idea what to do! :( If someone could please answer the question with a full solution so i can understand it i would be most grateful!!!

Thank you very much!

Apr 23rd 2007, 04:37 PM

Soroban

Hello, LoveDeathCab!

Quote:

Solve: .x^6 + 26x^3 - 27 = 0

Sure, you know what to do . . . try to factor it . . .

We have: .(x³ - 1)(x³ + 27) .= .0

Then solve the two equations:

. . x³ - 1 .= .0 . → . x³ = 1 . → . x = 1

. . x³ + 27 .= .0 . → . x³ = -27 . → . x = -3

Apr 23rd 2007, 04:39 PM

LoveDeathCab

Oh my goodness!

You are a genius! Thank you sooooo much! It was doing my head in! I feel rather stupid now! Haha thanks!

Apr 23rd 2007, 06:25 PM

topsquark

Quote:

Originally Posted by LoveDeathCab

Hey, i have to complete an AS level core one maths exam paper but i am completely stuck on the following question: Solve the equation x6+26x3-27=0

I have nooooo idea what to do! :( If someone could please answer the question with a full solution so i can understand it i would be most grateful!!!

Thank you very much!

Quote:

Originally Posted by Soroban

Hello, LoveDeathCab!

Sure, you know what to do . . . try to factor it . . .

We have: .(x³ - 1)(x³ + 27) .= .0

Then solve the two equations:

. . x³ - 1 .= .0 . → . x³ = 1 . → . x = 1

. . x³ + 27 .= .0 . → . x³ = -27 . → . x = -3

I am surprised that Soroban did not mention this: you are missing 4 complex solutions here. (Perhaps the "AS level core exam" means something to him. It doesn't to me!) If you want them, this is how to get them: